Analytical measuring and evaluation method for molecular interactions

ABSTRACT

The invention relates to an analytical measuring and evaluation method for determining the interaction parameters between an analyte and a ligand, preferably in a biosensor. According to the inventive method, the concentration of the analyte is gradually changed at defined intervals t i  and the initial association or dissociation rates or association and dissociation constants are determined. The invention further relates to a device for carrying out the inventive method.

AREA OF APPLICATION

[0001] The invention refers to a measurement and evaluation method fordetermining interaction parameters between an analyte and a ligand, forexample including rate constants or binding partner activities. Themeasured values are acquired, for example, with biosensors in which a(generally immobilized) first binding partner (ligand L) has a secondbinding partner (analyte A) added to it, and formation of theligand-analyte complex LA is detected as a function of time.

TECHNICAL BACKGROUND

[0002] So-called biosensors for detecting the time courses of theformation of analyte-ligand complexes are known in a wide variety ofembodiments, and other apparatuses, for example including array systems,are also usable for detecting such reactions. What are detected are boththe time courses of the association of the analyte on the ligand whenthe analyte concentration is increased by adding an analyte solution ofa specific concentration, as well as the dissociation upon addition of alower-concentration solution or one of zero concentration. In general,the time course of complexation is described using the function R(t) orR_(t), the concentration of the complex or its change over time beingreferred to as c_(t)(LA) or dc_(t)(LA)/dt. To a first approximation, afirst-order exponential curve is assumed for the time course of functionR, with exponent k_(on) upon association and k_(off) upon dissociationof the complex. It has hitherto been usual, for detection of thesevalues, to measure the reaction, e.g. the complexation, partially, oruntil attainment of an equilibrium value R_(eq) at which association ofthe analyte+ligand complex is in equilibrium with its dissociation.Dissociation of the complex, and a regeneration and washing phase, thenfollow. This is a very time-consuming process, especially when multiplemeasurements with different concentration changes need to be performedsuccessively. A further evaluation of the exponents that have beenobtained yields the actual kinetic rate constants of interest, but themethod requires a constant analyte concentration.

[0003] In existing methods for evaluating the measured values, it isusually assumed that the concentration of the analyte added to theligand is constant, despite complexation. This is approximated, forexample, by having the analyte concentration be many times greater thanthe ligand concentration, or by continuous exchange in the flowthroughsystem. In actuality, however, a depletion of the analyte or aconcentration change always occurs, for example, in the context ofassociation in the cuvette system, with the result that the equilibriumvalue R′_(eq) that is actually attained differs from the hypotheticalvalue R_(eq) at a constant analyte concentration. Although analysis ofthe measured values with a second-order approximation function yields amore accurate value for the coefficient of the exponential function, itis nevertheless complicated and requires additional determination orconsideration of a number of experimental boundary conditions.

[0004] Initial rates are employed for concentration determination. Theinitial rates are obtained by placing a compensation line at thebeginning of the association curve; its slope underestimates the initialrate, however, since the straight line does not take into account thecurvature of the curve. It is also known that when plotting the initialrates on a diagram against the analyte concentration c(A), in a contextof multiple measurements with different concentrations each time, intheory a straight line through the origin, with slope R_(max)*k_(ass),is obtained, R_(max) being the maximum possible reaction e.g. of thebiosensor to addition of an excess of an analyte. The slope of thisstraight line is, however, also distorted by the underestimate mentionedabove, so that this type of diagram is not employed for determiningk_(ass).

[0005] The measured values are detected using, inter alia, biosensors onthe flowthrough principle or cuvette principle, a very wide variety ofmeasurement methods being known in the existing art. In flowthroughsystems, a sensor surface on which the ligand is immobilized is impingedupon, for each analysis, by a constant flow of an analyte solution. Theapproximation of a preselected constant analyte concentration is appliedhere. In cuvette systems, a measurement cell is filled with an analytesolution and the reaction with the ligand on a sensor surface isdetected. Distortion of the measurement results occurs here inparticular, since actual reactions cause the analyte concentration tochange. When multiple measurement operations with differentconcentrations are being performed in succession, normally the cuvetteis purged with a buffer solution or otherwise regenerated, and then asolution with a different concentration is introduced.

[0006] In the context of multiple titrations, i.e. changes inconcentration, the measurement curves have hitherto been recorded untilcomplexation has reached an equilibrium state. Only the equilibriumstates, and not the kinetics or initial rates, are used for thedetermination of further variables. Access to the kinetics is in factexplicitly ruled out with multiple-step titrations of this kind.

[0007] For flowthrough systems, so-called sample loops arrangedsequentially behind one another, which are filled successively and canbe purged out into the measurement chamber, are known. The sample loopseach have, however, a volume that is exactly defined in a manner that islaborious in terms of production engineering, and between them anundefined extra volume also called the “dead volume.” Undesirable mixingof different solutions can occur in the dead volume. The loops cannot befilled from their outlet side, or partially, or even independently ofone another; and they cannot be purged into the measurement chamberindependently of one another.

DESCRIPTION OF THE INVENTION

[0008] a) Object

[0009] Proceeding from the existing art, it is the object of theinvention to describe a method with which measurement times for thedetection of measured values during complexation can be shortened,actual conditions during complexation (i.e. change in analyteconcentration) are taken into account, and multiple measurements can beperformed in succession, e.g. in a cuvette, without laborious purgingoperations; and which makes it possible to ascertain the kineticconstants from the initial rates and, under ideal conditions, also fromthe curve exponents.

[0010] b) Manner of Achieving the Object

[0011] According to the present invention, this object is achieved bythe method features of claim 1 and the apparatus features of claim 13.

[0012] Advantageous embodiments of the invention are the subject of therespective dependent claims.

[0013] The fundamental idea of the invention is that the change inanalyte concentration is taken into account during both association anddissociation of the complex. As a result, the function R assumes anequilibrium value R′_(eq) that differs from the value R_(eq). Duringassociation, i.e. addition of a higher-concentration analyte to theligand, a depletion of the analyte occurs during association, the resultbeing that R′_(eq) is less than the theoretical value R_(eq). At thefirst moment of the reaction, however, i.e. when the analyte solution isintroduced e.g. into the cuvette of a biosensor, the initial rate offunction R is independent of whether, later on, an analyte depletionoccurs due to binding of the analyte to the ligands, or a constantanalyte concentration is assumed. At time t=0, no reaction betweenanalyte and ligand has yet taken place. The fact that the actualreaction profile is taken into account also causes the exponentialcoefficient to change from k_(on) to k_(off). In reality, however, therelationship between the individual variables of the exponentialfunction is retained, i.e.: $\begin{matrix}{{{k_{on}^{\prime}*R_{eq}^{\prime}} = \frac{{R_{ass}\left( {t = 0} \right)}}{t}}{and}} & (1) \\{{k_{off}^{\prime}*\Delta \quad R^{\prime}} = \frac{{R_{diss}\left( {t = 0} \right)}}{t}} & (2)\end{matrix}$

[0014] where ΔR′ is the difference between the equilibrium value fordissociation and the starting value R_(st) of function R.

[0015] This means that, for example, the initial rate can be ascertainedfrom the actual measured values. This is also true if the exponentialfunction proceeds on a first-order basis but with two coefficientsk′_(on(1)) and k′_(on(2)), the two corresponding initial rates adding upto a overall rate.

[0016] It is possible in the context of the invention for the measuredcurve of function R to be recorded until the equilibrium value R′_(eq)is reached, in order, e.g. using a mathematical program, to ascertainthe exponents k′_(on) or k′_(off) and, from them, the initialassociation or dissociation rates. Preferably, only a portion of thecurve is acquired; for example, acquisition of function R can bediscontinued at an earlier point in time so as to ascertain theequilibrium situation from an extrapolation of the partial curve. Theexponent k is obtained using a nonlinear approximation, but can also bedetermined by linear regression of the derivative of function R.

[0017] From the initial rates, the respective association anddissociation rate constants k_(ass) and k_(diss) can be ascertainedusing $\begin{matrix}{\frac{{R_{ass}\left( {t = 0} \right)}}{t} = {k_{ass}*R_{\max}*{c_{0}(A)}}} & (3)\end{matrix}$

[0018] for the case of complex association, with a starting analyteconcentration c₀(A); and $\begin{matrix}{\frac{{R_{diss}\left( {t = 0} \right)}}{t} = {k_{diss}*\left( {- R_{st}} \right)}} & (4)\end{matrix}$

[0019] for the case of complex dissociation, the variable R_(st)indicating the starting value of function R during dissociation. Thestarting concentration c₀(A) is generally defined externally byexperiment.

[0020] The advantage of the invention is that a measurement can beperformed several times in succession, e.g. in a cuvette, with astepwise modification of the analyte concentration each time; it is notnecessary to complete each measurement to the point of reaching theequilibrium value, but instead it can be interrupted earlier and theconcentration of the analyte can be raised or lowered. It is alsopossible to perform measurement series with repeated (and alsoalternatingly successive) increases and decreases in analyte, in orderto acquire association and dissociation curves.

[0021] Although the starting rates of multiple i-fold association stepsare obtained from the sum of the previous and the new association, thenet starting rates of the respective association steps can beascertained, based on equations (1) and (3) stated above forassociation, using

k′ _(on,i)*(R′ _(eq,ass,i) −R′ _(st,ass,i))=(dR _(ass,i) /dt)_(t=0)  (5)

[0022] and

(dR _(ass,i) /dt)_(t=0)−(dR _(ass,i,−1) /dt)_(t=st,ass,i)=(dR_(ass,i,net) /dt)_(t=0)  (6)

[0023] and can be evaluated using

(dR _(ass,i,net) /dt)_(t=0) /c _(0,i,net)(A)=−k _(ass) *R _(st,ass,i) +k_(ass) *R _(max)  (7)

[0024] which corresponds to a straight-line equation and can be plottedaccordingly.

[0025] The quotient of the initial net association rate and net startinganalyte concentration, plotted against the starting association signalR_(st,ass,i), yields, when fitted linearly, a straight line having aslope −k_(ass) and an X-axis intercept R_(max). The individual phases ofmultiple dissociation steps from cuvette systems can be evaluateddirectly using equations (2) and (4) for dissociation.

[0026] So-called fit curves, with which the measurement results obtainedcan be approximated or (if the measurement is discontinued at an earlystage) extrapolated, are calculated using mathematical approximationprograms which ascertain a first- or higher-order exponential function,or even double exponential function, that approximates the measurementresults with the greatest possible accuracy. A curve of this kind can beautomatically calculated during the measurement by the evaluation unite.g. of a biosensor.

[0027] The stepwise modification of the concentration in the measurementchamber can be accomplished at any desired points in time duringacquisition of the measurement results. Especially recommended, however,is the half-life point of function R, at which the function, for examplein the context of an association, has attained half its final valueR_(eq).

[0028] If the derivative of function R(t) is plotted on a diagramagainst function R(t), what is obtained, if the plotted values areapproximated e.g. with a linear regression, is a straight line whoseY-axis intercept corresponds exactly to the initial rate, which also, inaccordance with equation (1), results from the absolute value of theline slope (−k′_(on)) and the X-axis intercept R′_(eq).

[0029] To simplify the evaluation, it is assumed that the reactionsproceed under ideal conditions, i.e. that, in particular, no analytedepletion occurs. This can be approximated, for example in the case ofbiosensors with flowthrough systems, by implementing a constant flowrate of solution in the measurement chamber, thereby simplifying theapproximation functions because, for example, a first-order exponentialfunction can be assumed for the profile of function R.

[0030] As stated by equation (3) above for determining the associationrate constant, it is also possible, if the other variables are known, todetermine the initial concentration c₀(A) of a solution that has justbeen introduced into a measurement chamber. For this purpose, forexample in a preceding series of experiments, a calibration line can becreated in accordance with an initial rate f(c₀(A)) with known c₀(A)values from the ascertained initial rates; the unknown c₀(A) value of asample can then be calculated from the calibration line using theinitial rate ascertained from the measured values.

[0031] It is also possible, especially when cuvette systems are beingused, to obtain the dissociation rate constant from the values obtainedfrom an association operation, and vice versa. The reason for this isthat, for example in the case of association, no dissociation is yetoccurring in the first moment at which the reaction begins. But becausefunction R assumes an equilibrium value at which association anddissociation are in equilibrium, this value also contains informationabout k_(diss). Reversing this approach results in an analogous resultfor dissociation. The corresponding equations are: $\begin{matrix}{k_{ass} = \frac{\frac{\left( {{R_{diss}}/{t}} \right)_{t = 0}}{\Delta \quad R_{{eq} - {st\_ diss}}}}{\left( \frac{c_{{eq}^{\prime}{\_ diss}}(A)}{R_{{eq}^{\prime}{\_ diss}}} \right)_{c_{{eq}^{\prime}{\_ diss}} = 0}R_{\max}}} & (8)\end{matrix}$

[0032] where ΔR_(eq-st) _(—) _(diss) corresponds to the differencebetween the final value (ideally zero) and the initial values of R fordissociation, c_(eq′) _(—) _(diss) is the concentration of A afterdissociation at equilibrium, and R_(eq′) _(—) _(diss) is the equilibriumvalue of R after dissociation, and the limit value for c_(eq′) _(—)_(diss)=0 is used in the denominator; and $\begin{matrix}{k_{diss} = \frac{\frac{\left( {{R_{ass}}/{t}} \right)_{t = 0}}{c_{0}(A)}}{\left( \frac{R_{{eq}^{\prime}{\_ ass}}}{c_{{eq}^{\prime}{\_ ass}}(A)} \right)_{R_{{eq}^{\prime}{\_ ass}} = 0}}} & (9)\end{matrix}$

[0033] with the corresponding values for association.

[0034] The method can also be utilized for evaluation with otheraffinity biosensors or array systems in solution, and with time-resolvedELISA or RIA techniques or other solid-phase-supported systems that areevident from the existing art.

[0035] In a cuvette system, in order to implement a constant flow ofsolution through the measurement chamber, the concentration of thesolution is kept constant by continuously adding and removing a portionof the solution. Present for that purpose, for example, are two hollowneedles with solutions, with which fresh solution is continuouslycirculated in the measurement chamber, or with which a portion of thesolution is continuously removed and then re-delivered in order tosimulate a flowthrough system with constant concentration.

[0036] In this case, as also in ideal flowthrough systems with aconstant concentration of solution in the measurement cell, function Ris approximated using a first-order exponential function, and thefollowing equation applies:

k′ _(on,i) =k _(ass) *c _(0,i)(A)+k _(diss)  (10)

[0037] where index i indicates the i-th stepwise change in concentrationin a multi-step experiment. With this method, both of the rate constantscan be ascertained from the same equation.

[0038] For ideal flowthrough systems with a starting analyteconcentration that is kept constant during an association phase, it hasbeen shown, as is known, that the starting concentration is exactlyequal to the dissociation equilibrium constant K_(p)=k_(diss)/k_(ass)if, at that concentration, half the immobilized ligand molecules arebound to analyte molecules, i.e. if ½ R_(max) has been attained. It canadditionally be demonstrated for such a case, however, that theassociation phase up to the point of attaining the equilibrium valuelasts exactly half as long as the subsequent dissociation phase forreturning back to the initial value of zero. At higher starting analyteconcentrations, association proceeds more quickly. With thisprecondition the dissociation curve, if it is overlaid on the previousassociation curve, intersects said association curve exactly at theGolden Section of the association equilibrium value, corresponding to avalue of 0.618 . . . * R_(eq) _(—) _(ass). In other words, the K₀ valuecan be extrapolated by applying different starting analyteconcentrations, and by subsequent regression to the intersectionmeasured value described above. Conversely, a starting analyteconcentration that is applied numerically in the K₀ value must yield themeasured intersection value just described; otherwise the interactionbeing recorded is not proceeding in ideal fashion. In principle,multi-step kinetics permits an analogous approach.

[0039] In general terms, especially for cuvette systems with a variableanalyte concentration in the measurement cell during a measurement step,the following equations additionally apply:

k′ _(on) =k _(ass) *c′ _(eqass)(A)+k′ _(off max)  (11)

[0040] with a line slope of k_(ass), in which c′_(eqass)(A) is theequilibrium analyte concentration after association, and k′_(offmax) themaximum value of the coefficient of the exponential function fordissociation; and

k′ _(off) =k _(diss)*(−R _(stdiss))/(R′ _(eq) −R _(stdiss))  (12)

[0041] with a line slope of k_(diss), the index “stdiss” denoting thestarting value for dissociation.

[0042] c) Exemplary Embodiments of the Biosensor

[0043] A biosensor known per se, equipped with a sensor surface on whichthe ligands are immobilized (i.e. bound), is used to carry out themethod. This binding can be accomplished, for example, as is known inthe existing art, by way of a chemical binding of the ligands or using areceptor matched to the ligands. A measurement chamber or cuvette thatcan be impinged upon by a solution of the analyte is configured abovethe sensor surface. A variety of measurement methods can be used todetect complexation (i.e. binding of the analyte to the ligand) and itschange over time, for example detecting the reflectivity of the backside of the sensor, which changes with the degree of complexation c(LA).A hollow needle, which is connected to the measurement chamber andeither delivers and/or draws out the solution, serves to introduce thesolution into the measurement chamber. The measurement chamber can alsobe equipped with two separate hollow needles for addition/removal.Impingement with a purging fluid through one of the hollow needles isalso possible. An apparatus for mixing the solution is present in orderto mix the solution in the measurement chamber, so as to preventconcentration gradients in the solution during the reaction; this canbe, for example, a vibratory stirrer. Equipping the biosensor with apreferably electronic control system and with suitable measurementdevices, in addition to data acquisition software, is evident from theexisting art.

[0044] According to the present invention, the biosensor is configuredin such a way that the solution in the measurement chamber is repeatedlyexchangeable, at least partially instantaneously, with solutions havingdifferent analyte concentrations, the liquid volume being keptsubstantially constant. This means that at least a portion of thesolution in the measurement chamber, or the entire solution, is removed,and a new solution having a different concentration is deliveredsubstantially simultaneously. By exchanging at least a portion of thesolution with another solution having a desired concentration, theoverall concentration in the measurement chamber is modified in definedfashion. The manner of exchanging the liquid can be embodied as desiredin the context of the invention, or it can be performed as set forthbelow. In a flowthrough system, the entire solution in the measurementchamber is exchanged; in a cuvette system, at least a portion thereof.The repeated exchange of the solution makes possible a stepwise changein the concentration in the measurement chamber, so that the methodaccording to the present invention can be carried out.

[0045] The advantage of the biosensor according to the present inventionis that, for example in cuvette systems, the volume of the solution iskept substantially constant and thus the number of parameters uponmathematical evaluation of the measurement results is decreased.Instantaneous exchange of the solutions moreover results, especially inflowthrough systems, in sharp transitions between individual associationand dissociation phases, which is necessary for determination of theinitial rates.

[0046] Exchange of at least a portion of the solution in the measurementchamber preferably takes place through one or more hollow needlessimultaneously. In particular, the solution is removed with one hollowneedle, and a new solution having an arbitrarily selectableconcentration is delivered using a different needle.

[0047] If the hollow needles are arranged separately from one another onthe measurement chamber, e.g. opposite one another, removal and deliverycan also be accomplished simultaneously; for complete exchange of thesolution in a cuvette system, removal and delivery are accomplished insuch a way that the measurement chamber is flushed out in order toprevent undesired residues from remaining behind. The hollow needles canalso be arranged coaxially, i.e. one extends inside the other, in whichcontext the inner one either removes or delivers the solution.

[0048] For conveying the solutions through the hollow needles into orout of the measurement chambers, pumps are provided with which thequantity of solution being conveyed in each case can be metered.So-called micropumps, which permit metering with the desired accuracy inorder to remove well-defined quantities of solution from the measurementchamber or deliver them thereto, are used for this purpose. These pumpscan be designed, inter alia, as tubing pumps, injection pumps, orpiezoelectric pumps; actuation is accomplished using actuating motors,electrical drives, etc. and they are also electronically controlled.

[0049] Mixing of the solution in the measurement chamber can also beaccomplished by the fact that using one or more hollow needles, aportion of the solution is drawn out and is immediately pumped back in,so that the solution is continuously circulated and mixed. Circulationis preferably performed at at least 1 μm/min in order to ensure ahomogeneous concentration of the solution in the measurement chamberduring complexation.

[0050] A further advantageous embodiment of the invention consists inthe fact that two or more so-called sample loops of arbitrary volume,which can be filled manually and/or automatically by means of a sampledispenser, are present in a specific fashion on the measurement chamber.The sample loops are preferably arranged in parallel between twomultiple selector valves, this entire arrangement being switchable intothe flow via a switching valve. The sample loops can thus be filled,outside the flow, on the one hand independently of one another becauseof the selector valves, and on the other hand, completely or onlypartially, for example in order to conserve analyte solution, from theiroutflow end via the switching valve. After filling, the solution of themost recently filled sample loop is present at the interface to the flowat the switching valve with no other intermediate volumes, i.e. with noso-called dead volume. This means that the measurement chamber can beimpinged upon in flowthrough fashion with multiple different solutionsfrom the individual sample loops via the selector valves successively,mutually independently, and with no dead volume, and with no need forany sample loop to be completely flushed out or for the flow to bedirected through it into another loop. A variable and instantaneous,stepwise, sample-economizing concentration change, with practically nomixing, is thereby ensured. In addition, the analyte concentration inthe solution in the measurement chamber can be kept constant in eachcase to a first approximation, in order to prevent depletion. Preferablya solution having a different concentration is present in each sampleloop, so that measurements with different concentrations can also beperformed in immediate succession, or in order to obtain, by controlledactivation of sample loops, an concentration intermediate between thevalues in the individual sample loops. The number of sample loops ispractically unlimited, although in the interest of greater flexibilitythe aforesaid entire arrangement, including the switching valve betweene.g. two two-way selector valves positioned in the flow, can readily beduplicated. The one set of sample loops can thus be processed while theother set is being filled, and can be switched into the flow, withpractically no dead volume, even before the last loop of the first sethas been completely flushed out.

[0051] A possible configuration of the sample feed system in, forexample, a flowthrough measurement system is reproduced in FIG. 1, whichis described below.

[0052] With the exception of pump 30, which can be e.g. an injectionpump or a peristaltic pump, all the other circles symbolize valves,which can be designed as described here. Valves 1 and 11 are switchingvalves to which the corresponding inlets or outlets of the valves areconnected depending on how the two switching positions are set; in FIG.1, the existing connections are shown with bold lines and thealternative connections with dashed lines. Valves 4, 8, 14, 18, 28 and,if desired, also 21, 22, 33, and 39 are selector valves with which acentral connector, depicted using a standard line width, can beconnected to one of an arbitrary number of other connectors. Valves 21,22, 33, and 39 are shown here, by way of example, as two-way selectorvalves. All the valve positions can be set manually or automatically,and also in preprogrammed fashion using e.g. an electrical or pressuredrive system. All the valves are preferably designed as the kind ofrotary valves used in chromatography, e.g. with a low-volume microdesign, but can also be designed e.g. as solenoid valves. 36 is anarbitrarily dimensionable temperature-control capillary, and 37 is theinteraction detection unit (called simply the “detector”), e.g. of theaffinity biosensor type. All the connections shown with a standard solidline comprise capillaries, made for example of Tefzel, PE, PEEK, orstainless steel, having arbitrary dimensions in terms of insidediameter/outside diameter/length, for example 1 mm/{fraction(1/16)}″/0.5 m for connection 31. A solution of any kind, selected fromreservoirs 25 through 27 or n additional ones, is pumped by means ofpump 30 either through valve 33 for purging purposes into waste vessel43, or through detector 37 and directed via valve 39 into waste vessel43. Solutions of further interest purged out of detector 37 can becollected via valve 39 in collector 41, retrieved in n fractions inmultiple containers, or coupled directly to other technologies, e.g.mass spectrometry. The components contained in C, surrounded with adot-dash line, can be temperature-controlled together e.g. by means of aPeltier element (not shown here).

[0053] What is particular to the present invention about this part isthe manner of feeding in the sample, which is advantageous forrepetitive sample feeding and in particular for multi-step kinetics.Components 1 through 10 are grouped together as sample feed system A,and can be switched either via valve 1 directly into connection 31 or,duplicated any number of times, via valves 21 and 22 into connections31/32; one duplication of A, grouped together with an analogous samplefeed system B, is depicted here. In A, valve 1 is in the loadingposition for sample loops 5 through 7, which can be filled via sampleinlet 2, either manually or automatically by means of a specimendispenser, with any desired solutions, i.e. also with analyte solutionsof respectively decreasing concentration, the displaced solutions beingpurged into waste vessel 10. Minimal volumes, e.g. for microanalyses ortest analyses, can be implemented by partially filling only connection3. Theoretically unlimited maximum volumes of a solution, e.g. forso-called preparations having particularly large sensor surfaces, can beimplemented by filling all the sample loops with the same solution.

[0054] After respectively synchronous switching of valves 4 and 8,sample loops 5 and 7 can be filled successively and mutuallyindependently and in each case completely or only partially (to conservesample), and in each instance “backwards,” i.e. from their later outletend. This ensures that after valve 1 has been switched into the flowposition, the solution of the most recent filling is present with nodead volume at connection 24 a; and that after the switching of valves 4and 8—at any point in time, stepwise, and synchronously in each case—thesolutions of the other sample loops can be allowed to impinge, with notransition and mutually independently, thereon and on detector 37. Thisimpingement is shown in B, where components 11 through 20 are in theflow position as a mirror image of A. By preferably synchronousswitching of valves 1, 11, 21, and 22, A and B can be alternatinglyswitched over into the flow and loading positions, so that A is in flowmode while B is being filled, and vice versa. All the connectingcapillaries and loops—3, 9, 13, 19, 23 a,b, 24 a,b, 29, 31, 32, 34, 35,38, 40, 42 and 5, 6, 7, 15, 16, 17—can be designed with particularlyoptimized dimensions depending on their application. Purge buffers orso-called run buffers from the last purging run or analytical run arenormally present in 24 a and/or 24 b. If necessary, these connectingcapillaries can also be designed with greater volumes so that, afterimpingement of the solutions from B or A and simultaneous switchover ofthe solutions from A or B into the flow position, a washing ordissociation phase can first be performed in detector 37, the durationthereof being determined by the volume of 24 a or 24 b and the flowrate; this may be of interest depending on the application. Thearrangement is moreover open for the positioning of further valvesand/or pumps for the purpose of washing or purging any desired portionsor for the introduction of further solutions. For example, B and/orfurther duplicates of B can optionally be positioned, via valve 11, e.g.in connections 3, 5, 6, 7, or 32.

[0055] Frequent switching of specific valves (different ones dependingon the application) furthermore makes possible a mixing of solutions, ifnecessary also by installation of a flow divider e.g. in connection 31instead of or in addition to valve 21, and/or of a so-calledmicro-mixing chamber e.g. in connection 32 instead of or in addition tovalve 22. The overall result of this arrangement is maximum flexibilityin terms of solution impingement upon the measurement cell. Mixing ofreservoirs 25 through 27 or others can also be achieved by frequentswitching of valve 28. For solutions that are temperature-sensitive, allor only some of the components contained in C, for example excluding thecomponents contained in D and surrounded with a dash-dot-dot line, canbe separately temperature-controlled, while the components e.g.contained in D can in turn be separately controlled to a workingtemperature.

List of Indices

[0056] ass Association

[0057] diss Dissociation

[0058] i i-th step

[0059] st Starting value of a particular association or dissociation

[0060] eq Equilibrium value of a particular association or dissociation

[0061] net Net

[0062] k_(on) Exponential coefficient for association

[0063] k_(off) Exponential coefficient for dissociation

1. An analytical measurement and evaluation method for molecularinteractions of chemical equilibrium binding pairs or binding systems,association and/or dissociation curves being acquired, and a firstbinding partner (“ligand”) having added to it a second binding partner(“analyte”), present in solution, which reacts reversibly with theligand accompanied by complexation, the development over time of thecomplexation and its change$\left( {{c_{t}({LA})};\frac{{c_{i}({LA})}}{t}} \right)$

being detected and the reaction course being described, to a firstapproximation, with an exponentially proceeding function R(t), having anexponent k′_(on), or k′_(off), that tends toward an equilibrium valueR′_(eq), $\frac{{R(t)}}{t}$

indicating the association or dissociation rate of the analyte on theligand, wherein at specific points in time t_(i) the concentrationc_(ti)(A) is raised or lowered, once or several times, stepwise; andfrom the respective differences between the equilibrium valuesR′_(eq,ass,i) and R′_(st,ass,i) or the differences between the valuesR′_(eq,diss,i) and R′_(st,diss,i) and the respective exponents k′_(on,i)or k′_(off,i), the respective initial association or dissociation rates,and from those rates the respective association or dissociation rateconstants k_(ass) or k_(diss), can be ascertained.
 2. The method asdefined in claim 1, wherein the change in concentration is accomplishedat the half-life point of the function R_(i)(t).
 3. The method asdefined in claim 1 or 2, wherein the initial association or dissociationrate is ascertained from a linear relationship between$\frac{{R(t)}}{t}$

and R(t) or (R(t)−R_(st)(t)).
 4. The method as defined in one of theforegoing claims, wherein the initial rates are ascertained using theassumption of ideal conditions, in particular the assumption that noanalyte depletion occurs upon association, and no analyte enrichmentupon dissociation.
 5. The method as defined in one of the foregoingclaims, wherein the unknown analyte concentration c₀(A) is ascertainedat the beginning of the reaction.
 6. The method as defined in one of theforegoing claims, wherein the dissociation rate constant k_(diss) isobtained from the initial association rates and the respectiveequilibrium association values of the function R(t), and the associationrate constant k_(ass) from the initial dissociation rates and therespective equilibrium dissociation values of the function R(t).
 7. Themethod as defined in one of the foregoing claims, wherein the method iscarried out with affinity biosensors and/or array systems in solutionand/or time-resolved ELISA or RIA techniques, known per se, or withother solid-phase-supported systems.
 8. The method as defined in one ofthe foregoing claims, wherein in a cuvette system, the concentration ofthe solution in the measurement chamber is kept substantially constantduring the association or dissociation process by continuous removal ofa portion of the solution and addition of a solution having acorresponding concentration through one or more hollow needles.
 9. Themethod as defined in one of the foregoing claims, wherein in the case ofa substantially constant analyte concentration in each case formulti-step analyses, the values for k_(ass) and k_(diss) are ascertainedfrom the relationship between k′_(on) and the starting analyteconcentration.
 10. The method as defined in one of the foregoing claims,wherein with a constant concentration of the solution in the measurementchamber, a determination is made of that c₀(A) value at which theassociation curve or a portion thereof intersects the dissociation curveor a portion thereof at the Golden Section of the overall associationvalue or the respective partial value.
 11. The method as defined inclaim 10, wherein the concentration in the measurement chamber ismodified repeatedly in steps, and the respective starting concentrationsof the analyte are ascertained.
 12. The method as defined in one of theforegoing claims, wherein the association rate constant k_(ass) isascertained from the relationship between k′_(on) and the equilibriumanalyte concentration, and the dissociation rate constant k_(diss) isascertained from the relationship between k′_(off) and the equilibriumvalue of the function R(t) during dissociation.
 13. An apparatus forcarrying out the method as defined in one of the foregoing claims,having a sensor surface for binding the analyte, present in solution, tothe ligand; having a measurement chamber on the sensor surface that isfilled with the analyte in solution; having a respective hollow needlefor the addition and/or removal of the solution and/or of a purgingfluid; having an apparatus for mixing the solution in the measurementchamber; wherein the solutions in the measurement chamber are, at leastpartially, instantaneously exchangeable several times in a predefinedquantity for solutions of a different concentration, the volume of thesolution being kept substantially constant.
 14. The apparatus as definedin claim 13, wherein exchange of the solutions in the measurementchamber takes place via one or more hollow needles, in particular onehollow needle removes the solution and another hollow needle adds a newsolution.
 15. The apparatus as defined in claim 13 or 14, wherein thehollow needles are arranged on the measurement chamber separately or onecoaxially inside the other.
 16. The apparatus as defined in one ofclaims 13 through 15, wherein one or more pumps, in particular tubingpumps, injection pumps, or piezoelectric pumps, are provided on thehollow needles for metering the quantity of solutions to be exchanged.17. The apparatus as defined in one of claims 13 through 16, wherein thesolution in the measurement chamber is mixed via multiple hollow needlesby at least partial withdrawal and re-addition into the measurementchamber, in particular at least 1 μl/min is circulated.
 18. Theapparatus as defined in one of claims 13 through 17, wherein multiplesample loops are present, and their contents can be introduced into themeasurement chamber independently and opposite to their fillingdirection; in particular, the sample loops are each filled withdifferent solutions.